Question

Determine X de modo que A (X, 20), B (2,3) e C (-1,-12) sejam colineares.

Answer 1

$\boxed{\boxed{\boxed{Ola\´ \: \: Kaitlyn} }}}$

Temos que os pontos são:
$\begin{cases} A (x, 20) \\ B(2,3) \\ C(-1,-12) \end{cases}$

Para que sejam colineares:
$\left| \begin{array}{ccc} x_A & y_A & 1 \\ x_B & y_B & 1 \\ x_C & y_C & 1 \end{array} \right| = 0$

Portanto, teremos:
$\left| \begin{array}{ccc} x & 20 & 1 \\ 2 & 3 & 1 \\ -1 & -12 & 1 \end{array} \right| = 0$
$\left| \begin{array}{ccc} x & 20 & 1 \\ 2 & 3 & 1 \\ -1 & -12 & 1 \end{array} \right| \: \left | \begin{array}{ccc} x & 20 \\ 2 & 3 \\ -1 & -12 \end{array} \right| = 0 \\ \Leftrightarrow (3x - 20 - 24) - ( - 3 - 12x + 40) = 0 \\ \Leftrightarrow 3x - 44 + 3 + 12x - 40 = 0 \\ \Leftrightarrow 3x + 12x= 44 - 3+ 40 \\ \Leftrightarrow 15x = 81 \\ \Leftrightarrow x = \frac{81}{15}$

$\Leftrightarrow \boxed{\boxed{x= \dfrac{27}{5}} }} \end{array}\qquad\checkmark$

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